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Prove that the tangent at a to the circumcircle of triangle abc is parallel to bc where triangle abc is a isosceles triangle?
Wiki User
∙ 14y ago
The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter, which is the point O, at which the perpendicular bisectors of the sides of the triangle are concurrent.
Since our triangle ABC is an isosceles triangle, the perpendicular line to the base BC of the triangle passes through the vertex A, so that OA (the part of the bisector perpendicular line to BC) is a radius of the circle O.
Since the tangent line at A is perpendicular to the radius OA, and the extension of OA is perpendicular to BC, then the given tangent line must be parallel to BC (because two or more lines are parallel if they are perpendicular to the same line).
Wiki User
∙ 14y ago
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What is the tangent if the sine is three fifths?
If the sine is 3/5, the tangent must be 3/4, and the triangle must be a 3-4-5 Pythagorean triangle.
If you divide length of the opposite side of an angle in a right triangle by the length of the adjacent side what value do you get?
It is a tangent.
Does a trigonometry tangent relate to a circle's tangent?
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.-------------------------------------------------------------------------------------------By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word). Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.
How do you find the apothem of an octagon with only the side length?
I wish I could draw or insert an octagon on this page. You draw an octagon, or do a google search for octagon and copy paste the image of the octagon on MS word. Set it so one side is horizontal. There should be another horizontal side on the top of the octogon. Draw an x by drawing line from the left end point of the top side to the right end point of the bottom side. Draw another line from the right end point of the top side to the left end point of the bottom side. The 2 lines intersect at the center of the octagon. If you continue drawing these lines you will have 8 triangles, each with a vertex angle equal to 1/8 of 360o. So, the vertex angle of each of the 8 isosceles triangles is 45o Look at the triangle whose base is the bottom side of the octagon The vertex angle at the top of this isosceles triangle is 45o. The sum of the interior angles of a triangle equals 180 o. The two base angles are equal. Let x equal the degrees of one of the base angles of the isosceles triangle. 2x + 45o = 180o 2x = 135o x = 67.5o Draw a line straight down from the center point of the octagon to the base of the triangle (bottom of octagon). This vertical line is the apothem. The apothem (vertical line) cuts the isosceles triangle into 2 right triangles. Now we can use trigonometry. Looking at the right triangle on the left side of the apothem, you know the left, bottom angle equals 67.5o and the apothem is the side opposite that angle. Tangent = Opposite ÷ Adjacent Adjacent is ½ of the length of the side of the octagon. Opposite is the apothem Example: Side length = 10cm ½ side length = 5 cm Angle = 67.5o Tangent 67.5o = Opposite ÷ 5cm Opposite = Tangent 67.5o × 5cm Opposite = 12.07 cm Or Since the apothem is perpendicular to the base of the isosceles triangle and bisects the base, it also bisects the vertex angle in to two angles of 22.5o. Therefore, in the right triangle with base the one half of the side s of the octagon and height the apothem a we have: a = (s/2)cot 22.5o In the above example, a = 5 cm (cot 22.5o) ≈ 12 cm
What is the tangent ratio for angle?
In a right angled triangle, it is the ratio of the lengths of the side opposite to the angle and the side adjacent to the angle.Of course, this definition restricts the function to (0, 90) degrees whereas the tangent function is defined for all real numbers.
What is the sine co sine and tangent of a 90 degree angle if it is on an isosceles right triangle?
0.602
Why is the tangent of 45 degrees 1?
That would be an isosceles right triangle with sides of 1, 1, and the square root of 2. 1/1=1.
What is the tangent side of triangle?
There can be no tangent side. The tangent of an angle, in a right angled triangle, is a ratio of the lengths of two sides.
What is the definition of the tangent ratio for a right triangle?
The tangent ratio for a right angle triangle is opposite/adjacent.
What is tangent in trigonometry?
Tangent is the ratio between perpendicular to the base of the triangle.
What is the tangent of a right triangle?
There is no such thing as the tangent of a triangle. Circles, angles, and conversations have tangents. In a right angled triangle, the tangent of one of the acute angles is the ratio of the length of the side opposite the angle to the length of the side adjacent to it.
What is the formula in getting a tangent?
For a right angle triangle: tangent = opposite/adjacent
Why is the tangent of 45 equals 1?
Let's look at an right isosceles triangle (where the base angles measure 45 degrees, and legs are congruent). So that, tan 45 degrees = leg/leg = 1
How do you find the length of the altitude to the base when an isosceles triangle has the base nagles of 30 degrees and base measures 12?
An isosceles triangle can be considered as two right angle triangles joined together so use the tangent ratio to find its altitude: tan30 degrees = opp/6 (where opp is the altitude and 6 is half the base) 6*tan30 degrees = 3.464101615 units of measurement
How do you find tangent parallel to line?
"tangent" meaning is a line or plane which touches a given curve or solid at a single point.Therefore, by definition there is no tangent to a line.if it were parallel it would not touch.if it were coincident it would touch in all places.
What is the tangent if the sine is three fifths?
If the sine is 3/5, the tangent must be 3/4, and the triangle must be a 3-4-5 Pythagorean triangle.
What is tangent 60degree angle of a triangle whose base 50meters and has ratios 1 2 sq root 3?
The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.The tangent of 60 degrees is sqrt(3) = 1.732 approx. The shape or size of the triangle is irrelevant.
